Seems like its pretty easy to prove that at least some of it is correct.
We cannot prove nor verify
any of Chainalysis's claims because their code and methods are complete black box.
Imagine the reputation Chainalysis would get if this went in their favor here. Let experts review their code, have their code independently validated, and then have their results form a central piece of evidence in such a high profile court case. They would be the only blockchain analysis company out there who could claim these accolades, and as a result would increase their customer base as well as being able to increase their prices. It's a perfect situation for them. All they have to do is let a few experts audit their code.
So why won't they let anyone look at their code? The potential upside for them is tremendous. It's almost like they know that this won't happen and instead their code will be torn to shreds and shown up for the absolute nonsense it is. What more can you expect from a company whose head of investigations doesn't know what a segwit address is or know the difference between bits and bytes.